Finite Group Databasebeta

← Group #13151321

Character table — Group #13151321

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11112222444446666666688121212121212121218181818181818181818181824242424242424242424363636363636363636363636363636363636727272727272
order122236662241212336666666636666666444444444444666666121212122244441212121212121212121212126612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111-1-1-1-1111111111-1111-1-111111-1-1111111-1-11-111-1-1-1-1-1-11-1-1-11-111-1-1111111-1-11-1-1-11-1
χ6111111111-1-1-1-1111111111-1111-1-111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-1111-111-11
χ7111111111-1-1-1-1111111111-1111-1-1111-1-1111111-1-1111-111-1-1-1-1-1-1-11-1-1-11-1-1111111-1-111-11-1-1-11
χ8111111111-1-1-1-1111111111-1111-1-1111-1-111-1-1-1-111-1-11-111-1-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-1-11111-1
χ911111111-11-1-1-111111111-111-1-11111111-1-111-1-11111-11-1-111-1-1-1-1-111-1-1-111-1-111-1-11111-111-1-1-1
χ1011111111-11-1-1-111111111-111-1-11111111-1-1-1-111-1-1-1-1-11-1-111-1-1-1-1-11-111111-1-1-1-111-1-1-1-1-11-1111
χ1111111111-11-1-1-111111111-111-1-111111-1-11111-1-1-1-1-1-1-11-1-111-1-1-1-11-11-111-1-11111-1-1-1-1-1-11-11-111
χ1211111111-11-1-1-111111111-111-1-111111-1-111-1-1111111-11-1-111-1-1-1-11-1-11-1-1-1-111-1-11111111-1-11-1-1
χ1311111111-1-111111111111-1-11-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11-11111111-1-111-1-1-1-1-11-11
χ1411111111-1-111111111111-1-11-1-1-1-11111111-1-111-1-111-1-1-1-1-1-11111-1-11-11-11111-1-111-1-111-1-11-11-1
χ1511111111-1-111111111111-1-11-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-111-1-1-1-1-111-1-1-1-11111-111-1
χ1611111111-1-111111111111-1-11-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1111-1-11
χ1722222222222222-122-1-12-122-122-1-1-1-1-1000000002222-12-1-1-1-12-1-1-100002200000000-1-1-1-10000-1-1
χ1822222222222222-122-1-12-122-122-1-1-1-1-100000000-2-2-2-2-12-1-1-1-12-1-1-10000-2-2000000001111000011
χ192222222222222-12-1-122-1222-1-1-122-1-1-10000222200002-1-1-1-1-1-12-1-10022000000-1-1-1-1000000-1-100
χ202222222222222-12-1-122-1222-1-1-122-1-1-10000-2-2-2-200002-1-1-1-1-1-12-1-100-2-200000011110000001100
χ21222222222-2-2-2-22-122-1-12-12-2-12211-1-1-10000000022-2-2-1-2-1-111-211100002-200000000-1-1110000-11
χ22222222222-2-2-2-22-122-1-12-12-2-12211-1-1-100000000-2-222-1-2-1-111-21110000-220000000011-1-100001-1
χ23222222222-2-2-2-2-12-1-122-122-2-1-1-1-2-2-1-1-100002222000021-1-1111-21100-2-2000000-1-1-1-10000001100
χ24222222222-2-2-2-2-12-1-122-122-2-1-1-1-2-2-1-1-10000-2-2-2-2000021-1-1111-21100220000001111000000-1-100
χ2522222222-22-2-2-22-122-1-12-1-22-1-2-2-1-1-1-1-10000000022221211-1-1-21110000-2-200000000-1-1-1-1000011
χ2622222222-22-2-2-22-122-1-12-1-22-1-2-2-1-1-1-1-100000000-2-2-2-21211-1-1-21110000220000000011110000-1-1
χ2722222222-22-2-2-2-12-1-122-12-22-11122-1-1-1000022-2-20000-2-111-1-11-211002-2000000-1-111000000-1100
χ2822222222-22-2-2-2-12-1-122-12-22-11122-1-1-10000-2-2220000-2-111-1-11-21100-2200000011-1-10000001-100
χ2922222222-2-22222-122-1-12-1-2-2-1-2-211-1-1-10000000022-2-21-211112-1-1-10000-2200000000-1-11100001-1
χ3022222222-2-22222-122-1-12-1-2-2-1-2-211-1-1-100000000-2-2221-211112-1-1-100002-20000000011-1-10000-11
χ3122222222-2-2222-12-1-122-12-2-2-111-2-2-1-1-1000022-2-20000-211111-12-1-100-22000000-1-1110000001-100
χ3222222222-2-2222-12-1-122-12-2-2-111-2-2-1-1-10000-2-2220000-211111-12-1-1002-200000011-1-1000000-1100
χ3322-2-22-22-200000222-22-2-2-200200002-2-2002-2002i−2i002i−2i0000000000000000002-2002i−2i002i−2i000000
χ3422-2-22-22-200000222-22-2-2-200200002-2-2002-200−2i2i00−2i2i0000000000000000002-200−2i2i00−2i2i000000
χ3522-2-22-22-200000222-22-2-2-200200002-2-200-22002i−2i00−2i2i000000000000000000-22002i−2i00−2i2i000000
χ3622-2-22-22-200000222-22-2-2-200200002-2-200-2200−2i2i002i−2i000000000000000000-2200−2i2i002i−2i000000
χ372-22-22-2-220000022-22-22-2-20020000-22-22-2002i−2i002i−2i0000000000000000002-2002i−2i002i−2i00000000
χ382-22-22-2-220000022-22-22-2-20020000-22-22-200−2i2i00−2i2i0000000000000000002-200−2i2i00−2i2i00000000
χ392-22-22-2-220000022-22-22-2-20020000-22-2-22002i−2i00−2i2i000000000000000000-22002i−2i00−2i2i00000000
χ402-22-22-2-220000022-22-22-2-20020000-22-2-2200−2i2i002i−2i000000000000000000-2200−2i2i002i−2i00000000
χ414444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111000000000000-2-21111-2-211000000000000000000000000
χ42444444444-4-4-4-4-2-2-2-2-2-2-2-24-41-2-222111000000000000-2211-1-122-1-1000000000000000000000000
χ4344444444-44-4-4-4-2-2-2-2-2-2-2-2-44122-2-21110000000000002-2-1-11122-1-1000000000000000000000000
χ4444444444-4-4444-2-2-2-2-2-2-2-2-4-41222211100000000000022-1-1-1-1-2-211000000000000000000000000
χ4544-4-44-44-4000004-24-4-22-4200-20000-22200000000004i−4i00000000000000000000000000−2i2i000000
χ4644-4-44-44-4000004-24-4-22-4200-20000-2220000000000−4i4i000000000000000000000000002i−2i000000
χ4744-4-44-44-400000-24-224-42-400-20000-2220000004i−4i00000000000000000000000000−2i2i0000000000
χ4844-4-44-44-400000-24-224-42-400-20000-222000000−4i4i000000000000000000000000002i−2i0000000000
χ494-44-44-4-44000004-2-442-2-4200-200002-22000000004i−4i00000000000000000000000000−2i2i00000000
χ504-44-44-4-44000004-2-442-2-4200-200002-2200000000−4i4i000000000000000000000000002i−2i00000000
χ514-44-44-4-4400000-242-2-442-400-200002-2200004i−4i00000000000000000000000000−2i2i000000000000
χ524-44-44-4-4400000-242-2-442-400-200002-220000−4i4i000000000000000000000000002i−2i000000000000
χ534-4-4444-4-40000044-4-4-4-4440040000-4-440000000000000000000000000000000000000000000000
χ544-4-4444-4-4000004-2-4-4224-200-200−2i32i322-20000000000000000−2i32i30000000000000000000000000000
χ554-4-4444-4-4000004-2-4-4224-200-2002i3−2i322-200000000000000002i3−2i30000000000000000000000000000
χ564-4-4444-4-400000-2422-4-4-2400-2−2i32i30022-200000000000000−2i32i3000000000000000000000000000000
χ574-4-4444-4-400000-2422-4-4-2400-22i3−2i30022-2000000000000002i3−2i3000000000000000000000000000000
χ584-4-4444-4-400000-2-22222-2-2001−2i32i3−2i32i3-1-1100000000000000i3−i3i3−i3003-3000000000000000000000000
χ594-4-4444-4-400000-2-22222-2-2001−2i32i32i3−2i3-1-1100000000000000i3−i3−i3i300-33000000000000000000000000
χ604-4-4444-4-400000-2-22222-2-20012i3−2i3−2i32i3-1-1100000000000000−i3i3i3−i300-33000000000000000000000000
χ614-4-4444-4-400000-2-22222-2-20012i3−2i32i3−2i3-1-1100000000000000−i3i3−i3i3003-3000000000000000000000000
χ626666-3-3-3-3666-3-300000000-3-3000000002222000000000000000000220000-1-1-1-100000000-1-10000
χ636666-3-3-3-3666-3-300000000-3-300000000-2-2-2-2000000000000000000-2-20000111100000000110000
χ646666-3-3-3-36-6-63300000000-330000000022-2-20000000000000000002-20000-1-11100000000-110000
χ656666-3-3-3-36-6-63300000000-3300000000-2-222000000000000000000-22000011-1-1000000001-10000
χ666666-3-3-3-3-66-633000000003-30000000022-2-2000000000000000000-220000-1-111000000001-10000
χ676666-3-3-3-3-66-633000000003-300000000-2-2220000000000000000002-2000011-1-100000000-110000
χ686666-3-3-3-3-6-66-3-30000000033000000002222000000000000000000-2-20000-1-1-1-100000000110000
χ696666-3-3-3-3-6-66-3-3000000003300000000-2-2-2-2000000000000000000220000111100000000-1-10000
χ7088-8-88-88-800000-4-4-44-444400200002-2-20000000000000000000000000000000000000000000000
χ718-88-88-8-8800000-4-44-44-4440020000-22-20000000000000000000000000000000000000000000000
χ721212-12-12-66-6600000000000000000000000004-400000000000000000000000000-2200000000000000
χ731212-12-12-66-660000000000000000000000000-44000000000000000000000000002-200000000000000
χ7412-1212-12-666-6000000000000000000000004-400000000000000000000000000-220000000000000000
χ7512-1212-12-666-600000000000000000000000-44000000000000000000000000002-20000000000000000
χ7612-12-1212-6-666000−6i36i30000000000000000000000000000000000000000000000000000000000000000
χ7712-12-1212-6-6660006i3−6i30000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).